Sketch the absolute vaule function. For each sketch state the intercepts,domain and range.
| -2/3 x-4 |
Unfortunately, I cannot sketch a graph here. However, I can provide you with the information you need.
The absolute value function | -2/3 x-4 | can be broken down into two separate cases: when -2/3 x-4 is positive and when -2/3 x-4 is negative.
Case 1: -2/3 x-4 is positive
In this case, the absolute value function is equal to -2/3 x-4.
Intercepts:
To find the x-intercept, set -2/3 x-4 equal to zero and solve for x:
-2/3 x-4 = 0
-2/3 x = 4
x = -6
To find the y-intercept, plug in x = 0 into the function:
-2/3 (0) - 4 = -4
Domain:
The function is defined for all real numbers.
Range:
The range of the function is all real numbers greater than or equal to -4.
Case 2: -2/3 x-4 is negative
In this case, the absolute value function is equal to -( -2/3 x-4 ) = 2/3 x + 4.
Intercepts:
To find the x-intercept, set 2/3 x + 4 equal to zero and solve for x:
2/3 x + 4 = 0
2/3 x = -4
x = -6
To find the y-intercept, plug in x = 0 into the function:
2/3 (0) + 4 = 4
Domain:
The function is defined for all real numbers.
Range:
The range of the function is all real numbers greater than or equal to 4.
So, the graph of the absolute value function | -2/3 x-4 | will have two intersecting lines at (-6, -4) and (-6, 4). The domain of the function is all real numbers, and the range is all real numbers greater than or equal to -4, except for the value 4.